Mathematics and statistics

Simply connected domain

A simply connected domain, also called 1-connected, is a region with no holes, where every closed loop shrinks to a point; this guarantees path-independent integrals in complex analysis and vector calculus.

Simply typed lambda calculus

The simply typed lambda calculus is a typed form of lambda calculus formulated by Alonzo Church in 1940, where every term has a type and all programs terminate.

Simpson's paradox

Simpson's paradox, also called the Yule–Simpson effect or reversal paradox, is a statistics phenomenon in which a trend seen in combined data reverses within every subgroup.

Simulated annealing

Simulated annealing (SA) is a probabilistic optimization method that occasionally accepts uphill moves as temperature falls, proposed by Kirkpatrick, Gelatt, and Vecchi at IBM in 1983.

Simulation of Lévy processes

Simulation of Lévy processes means generating sample paths from the triplet that characterizes the process, trivial for jump-diffusions and hard otherwise, using truncation, series representations, and Euler schemes.

Simulation optimization

Simulation optimization, also called optimization via simulation (OvS), is a family of operations research methods that finds the best input settings of a stochastic simulation.

Simultaneous equations model

A simultaneous equations model is a statistical model in which several dependent variables are determined jointly, as when price and quantity determine each other in a market.

Simultaneous inference

Simultaneous inference is the family of statistical methods for testing several hypotheses in one analysis while controlling an overall error rate, such as the family-wise error rate.

Sinc function

The sinc function, also called the cardinal sine (sinus cardinalis), is defined as sin(x)/x with sinc(0) = 1, and is the Fourier transform of a rectangular pulse.

Sine and cosine

Sine and cosine, also written sin and cos, are the two fundamental trigonometric functions, taking any real input, returning values between −1 and 1, and repeating every 2π.

Single and double layer potentials

Single and double layer potentials write solutions of elliptic partial differential equations as surface integrals over a domain's boundary, using a fundamental solution and a density.

Single point of failure

A single point of failure (SPOF), also called a central point of failure, is any component whose own failure stops a system or critical function from operating.

Single-precision floating-point format

Single-precision floating-point format, also known as binary32 or Float32, is a 32-bit IEEE 754 format for approximate real numbers, the default in graphics and machine learning.

Singleton bound

The Singleton bound is an upper limit on the minimum distance of an error-correcting code: a code of length n, dimension k, and distance d satisfies d ≤ n − k + 1.

Singular (software)

Singular is a free, open-source computer algebra system for polynomial computations, developed at the University of Kaiserslautern with special emphasis on commutative algebra, algebraic geometry, and singularity theory.

Singular homology

Singular homology is a construction in algebraic topology that assigns to every topological space abelian groups measuring its connectedness and holes, defined by Samuel Eilenberg in 1944.

Singular matrix

A singular matrix, also known as a degenerate matrix, is a square matrix with determinant zero and no multiplicative inverse, so Ax = b may lack a unique solution.

Singular series

The singular series is an Euler product over primes, chiefly in the Hardy–Littlewood prime k-tuple conjecture and circle method, correcting a naive random model for local obstructions.

Singular solution

A singular solution of a differential equation is a solution not obtainable from the general solution by assigning any value to its arbitrary constant, such as the envelope of Clairaut's equation.

Singular spectrum analysis

Singular spectrum analysis (SSA) is a nonparametric method, describable as PCA applied to time series, that decomposes a series into trend, oscillations, and noise for denoising, forecasting, and trend extraction.

Singular value

A singular value of a matrix or linear operator is a non-negative real number measuring how much it stretches space; singular values form the singular value decomposition.

Singular value decomposition

The singular value decomposition (SVD) is a factorization of any real or complex matrix A into A = U Σ Vᵀ, with orthogonal matrices and nonnegative singular values.

Singular value thresholding

Singular value thresholding (SVT) is a first-order iterative algorithm for minimizing the nuclear norm of a matrix, introduced by Cai, Candès, and Shen in 2010, whose leading application is matrix completion.

Singularity

In mathematics, a singularity, or singular point, is a point where an equation, surface, or mapping blows up, fails to be defined, or becomes degenerate.

Singularity analysis

Singularity analysis is a technique of analytic combinatorics, presented by Philippe Flajolet and Andrew Odlyzko in 1990, that derives asymptotic estimates of a generating function's coefficients from its dominant singularities.

SIPOC

SIPOC is a diagram used in Six Sigma's Define phase to summarize a process as suppliers, inputs, process, outputs, and customers, agreeing scope before detailed flowcharting.

Oct 22, 2026

SISSO

SISSO, short for sure independence screening and sparsifying operator, is a materials-informatics algorithm using symbolic regression and compressed sensing to find short formulas that predict material properties.

Six operations

The six operations are a system of six interrelated functors, developed by Grothendieck in his duality work, that attach to categories of geometric objects such as schemes.

Six Sigma

Six Sigma is a data-driven method for improving business processes by reducing variation and defects, targeting 3.4 defects per million opportunities. Motorola developed it in 1986, and it is applied through the five-phase DMAIC cycle.